Measuring Doppler Shift Using Sound
Written by George J. Bendo, UK ALMA Regional Centre Node
Version: October 2015
Overview
In this experiment, we will make measurements of the change in frequency of sound waves
from a sound source that is moving relative to the microphone. One person will run with a
sound source along a measured distance, a second person will time the runner, and the third
person will measure the change in frequency of the sound source. We will then use this to
estimate the velocity of the moving sound source, which we can then compare to what we
measure using a tape measure and a stopwatch.
Introductory Science Concepts
When a source producing either sound waves or electromagnetic waves (including radio
wave and visible light) is stationary, those waves will appear to be the same frequency no
matter which direction they are viewed in. However, when the source moves, the waves will
appear different depending on how the object is observed. When the emitting object is
moving towards the observer, the waves will appear bunched together, and the frequency of
the waves will get higher. When the emitting object is moving away from the observer, the
waves will get stretched out, and the frequency will get lower. This phenomenon is called
Doppler shifting.
In everyday life, Doppler shifting can be experienced in a variety of settings. The most
common example is the tone of the siren from a police car or ambulance as it drives by on
the street. When the vehicle is approaching, the siren sounds higher pitched than when it is
travelling away. Radar devices use the Doppler shifting of radio waves to determine the
speed at which objects (including airplanes, cars, and clouds) are moving.
In astronomy, Doppler shifting is commonly used to measure the velocities at which stars,
nebulae, and galaxies are moving. The spectra of starlight contain dark absorption lines
found at specific wavelengths created by atoms and molecules in the outer atmospheres of
the stars. The spectra of interstellar gas contain bright emission lines from the atoms and
molecules in the gas. When the stars or gas move, these absorption and emission lines
shift, and astronomers can compare the measured frequencies of these lines to the
expected frequencies when the objects are at rest to determine how quickly the objects are
moving.
As a side note, when astronomers look at the spectra of galaxies, the Doppler shifting of the
lines shows that the galaxies are moving away from us. Furthermore, more distant galaxies
appear to be moving away faster than nearby galaxies; the distances can be related by the
equation
v = H0d
(1)
where H0 is the Hubble constant. Since light appear redder when the galaxies move away,
astronomers normally refer to the Doppler shift for galaxies as the redshift. They can use
the redshift as a substitute for distance. This phenomena demonstrated that the universe is
expanding and led astronomers to determine that the universe must have formed in an
explosion now called the Big Bang.
Science Concepts in This Experiment
In this experiment, we will measure the velocity vsource of a running person holding a sound
source using two different techniques.
First, we will measure the velocity of the runner by measuring the amount of time Δt it takes
for the runner to cross between two points separated by a distance Δd. The velocity is given
by
vsource = Δd/Δt.
(2)
Second, we will measure the velocity of the runner by measuring the shift in the frequency of
the sound waves from the sound source. When the sound source is at rest, it will produce
sound at a constant frequency that we will refer to as the rest frequency f rest. When the
sound source is moving relative to the observer, the observed frequency fobs will change
depending on whether the source is moving towards or away from the observer. When the
sound source is approaching the observer, the observed and rest frequencies are related by
vsource = vsound(1-frest/fobs),
(3)
and when the sound source is moving away from the observer, the relation between the
frequencies is given by
vsource = vsound(frest/fobs-1),.
(4)
In these equations, vsound is the speed of sound, which is 343 m/s at 20° C.
Equipment
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Sound source – You can use a smartphone with a tone generator app. Many such
apps can be either purchased or downloaded for free for Android and Apple devices;
we use Tone Generator Pro on an iPod Touch.
One high-sensitivity microphone – This should be a highly amplified microphone, not
standard microphones. We use a Sonic Sleuth microphone, but this microphone and
similar microphones are also sold under other names (such as Bionic Ear and Sonic
Explorer).
Audio cable
Computer with frequency analysis software – You need a program that can plot
sound intensity versus frequency, We are using Spectrum Lab by Wolfgang Büscher
(http://www.qsl.net/dl4yhf/spectra1.html) on a laptop running Windows 8. This
software is free.
Tape measure or ruler
Timer
Procedure
1. Find a space where someone can run several meters. This experiment may need to
be set up outdoors, in a gym, or in a long hallway. Measure a distance (such as 5 m)
over which you will measure a person running with the sound source. Mark the end
points of these locations.
2. Turn on the computer and start the sound analysis program. The program needs to
be set up to show the intensity of the sound as a function of frequency.
3. Plug the microphone into the computer. The microphone should be set up about 1 m
from the finish point.
4. Turn on the sound source and set the frequency. A frequency between 1500-2000
Hz works well for this experiment.
5. Measure the frequency of the sound when the sound source is stationary. The
sound wave should appear as an intensity spike. Zoom in on the frequency where
the intensity spike is seen; you want to display a range of 40-50 Hz with the intensity
spike in the middle.
6. Simultaneously have three people do the following:
a. One person should run with the sound source towards the microphone. It
would be good if the person starts running about 1 or 2 m before reaching the
start point so that he is at full speed when he passes between the start and
finish points.
b. One person should time the runner as he passes between the start and finish
points.
c. One person should measure the maximum frequency of the sound source
when the runner passes between the points. This will be the maximum
frequency of the location of the intensity spike displayed by the sound
analysis software. If possible, the frequency should be measured to 4
significant figures.
7. Repeat step 6 several times.
8. Repeat step 6 several times, but this time, the runner should run away from the
microphone. In this case, the person measuring the frequency should measure the
minimum frequency of the sound source.
9. Use Equations 3 and 4 to calculate the velocity of the runner in each trial. Compare
this to the velocity that you measure using Equation 2.
Additional Exercises
1. Try repeating the experiment with a different frequency (one that is 2 times higher or
lower in frequency). Do you get the same answer?
2. Instead of comparing the velocities, solve Equations 2, 3, and 4 for the speed of
sound.